## Geometry & Topology

### Hyperbolic jigsaws and families of pseudomodular groups, I

#### Abstract

We show that there are infinitely many commensurability classes of pseudomodular groups, thus answering a question raised by Long and Reid. These are Fuchsian groups whose cusp set is all of the rationals but which are not commensurable to the modular group. We do this by introducing a general construction for the fundamental domains of Fuchsian groups obtained by gluing together marked ideal triangular tiles, which we call hyperbolic jigsaw groups.

#### Article information

Source
Geom. Topol., Volume 22, Number 4 (2018), 2339-2366.

Dates
Revised: 23 June 2017
Accepted: 9 October 2017
First available in Project Euclid: 13 April 2018

https://projecteuclid.org/euclid.gt/1523584824

Digital Object Identifier
doi:10.2140/gt.2018.22.2339

Mathematical Reviews number (MathSciNet)
MR3784523

Zentralblatt MATH identifier
06864339

#### Citation

Lou, Beicheng; Tan, Ser Peow; Vo, Anh Duc. Hyperbolic jigsaws and families of pseudomodular groups, I. Geom. Topol. 22 (2018), no. 4, 2339--2366. doi:10.2140/gt.2018.22.2339. https://projecteuclid.org/euclid.gt/1523584824

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